This chapter presents the methodology for the optimum design of one-way reinforced concrete (RC) slabs cast on top of textile-reinforced concrete (TRC) stay-in-place (SiP) formwork elements. The latter are considered to participate to the structural behavior of the composite slabs. The optimization procedure results in the derivation of minimum production cost design solutions, which satisfy the Ultimate Limit State (ULS) and serviceability limit state (SLS) performance criteria. A set of critical design parameters comprise the design solution. These parameters are: the shape and geometric characteristics of formwork's section, the effective depth of textile reinforcement in the composite slab, and the steel and textile reinforcement ratio. The main benefit from the procedure is that the results indicate critical design criteria for each span and design load level. Thus, the results highlight the critical issues for future experimental investigation. The solution of the optimization problem is attained through the development of a computer program using a genetic algorithm provided by Matlab®. For the description of cementitious composite's tensile behavior, an effectiveness coefficient is utilized. This accommodates all the mechanisms’ factors which deteriorate the performance of textile reinforcement in the cementitious composite. Finally, closed-form expressions for the determination of critical design values are presented.
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